A coupling modeling method for rocket liquid hydrogen filling system based on gas state equation

Abstract

This invention discloses a coupled modeling method for a rocket liquid hydrogen refueling system based on the gas state equation, belonging to the field of launch vehicle propellant refueling technology. The method establishes a pressurization model of the ground storage tank's gas pillow and a depressurization model of the onboard tank's gas pillow. Based on the gas state equation, the gas pillow state is characterized, and the gas mass changes on both sides of the gas pillow are determined to solve for the gas pillow pressure. A model relating liquid level to gas pillow volume is established, calculating the liquid level changes on both sides based on the main refueling flow rate and vaporization flow rate to obtain the gas pillow volume. A flow calculation model for the delivery pipeline is established, determining the available pressure difference in the pipeline based on the gas pillow pressure, liquid level static pressure, and position altitude to calculate the main refueling flow rate. A dynamic equation set is constructed and numerically solved to obtain the dynamic parameters of the entire refueling process. This invention incorporates the ground storage tank, vaporizer, delivery pipeline, and onboard tank into a unified model, achieving dynamic simulation of the entire liquid hydrogen refueling process and providing a model foundation for refueling process analysis, parameter adjustment, and operational control.

Description

Technical Field

[0001] This invention relates to the field of rocket propellant refueling technology, and in particular to a coupled modeling method for rocket liquid hydrogen refueling systems based on the gas equation of state. Background Technology

[0002] The liquid hydrogen refueling system at a space launch site is used to transfer liquid hydrogen from ground storage tanks to the onboard propellant tanks according to a predetermined process before launch. Liquid hydrogen is characterized by its low temperature, low density, easy vaporization, and sensitivity to heat input and pressure changes. Therefore, the refueling process involves not only the delivery of liquid propellant but also multiple physical processes such as changes in tank pressure, vaporization pressurization, pipeline resistance, valve regulation, changes in liquid level in the onboard propellant tanks, and gas emission. These processes interact with each other, giving the liquid hydrogen refueling system a distinct dynamic coupling characteristic.

[0003] Existing technologies have included analyses of issues such as filters, two-phase flow in cryogenic pipelines, heat leakage faults, and visualization simulations of the refueling process in liquid hydrogen refueling pipelines. For example, some studies focus on the impact of local components like filters on the pipeline flow field and pressure drop; others focus on two-phase flow and phase change phenomena within cryogenic pipelines; still others focus on the impact of heat leakage faults on liquid hydrogen refueling and rocket launch missions, or simulate the refueling process using augmented reality and other methods. These studies provide references for component analysis, fault identification, and operational simulation of liquid hydrogen refueling systems.

[0004] However, the aforementioned technologies mostly focus on local pipe sections, local components, specific faults, or visualization, and are still difficult to directly form a holistic dynamic coupled model that can simultaneously describe the pressure of the ground tank gas pillow, the vaporization pressurization flow rate, the pressure difference of the delivery pipeline, the liquid level of the onboard tank, the pressure of the onboard gas pillow, and the depressurization process. Especially during the refueling process, the decrease in the liquid level of the ground tank changes the volume of the ground gas pillow, the vaporization branch changes the gas mass within the ground gas pillow, the increase in the liquid level of the onboard tank compresses the volume of the onboard gas pillow, and the onboard depressurization channel discharges some gas to suppress pressure rise; these factors collectively determine the main refueling flow rate and system pressure changes. Without a unified coupled modeling method, it is difficult to continuously simulate and analyze the trends of pressure, liquid level, and flow rate changes during the refueling process. Summary of the Invention

[0005] The purpose of this invention is to provide a coupled modeling method for rocket liquid hydrogen refueling systems based on the gas state equation. This method incorporates ground storage tanks, vaporizers, delivery pipelines, and onboard tanks into a unified model. By coupling the gas cushion state equation, liquid level change equation, pipeline pressure difference equation, and flow resistance equation, dynamic simulation of the entire liquid hydrogen refueling process is achieved, providing a model basis for refueling process analysis, parameter adjustment, and operation control.

[0006] To achieve the above objectives, this invention provides a coupled modeling method for a rocket liquid hydrogen refueling system based on the gas equation of state, comprising the following steps: S1. Establish a pressurization model for the gas pillow of the ground storage tank: characterize the state of the gas pillow of the ground storage tank based on the gas state equation, determine the gas mass change of the gas pillow according to the vaporization flow rate of the vaporization branch, and solve the gas pillow pressure of the ground storage tank by combining the dynamic change of the gas pillow volume. S2. Establish a pressure relief model for the air cushion of the rocket's onboard storage tank: characterize the state of the air cushion of the rocket's onboard storage tank based on the gas state equation, determine the change in the mass of the air cushion gas based on the discharge flow rate of the pressure relief channel, and solve the pressure of the air cushion of the rocket's onboard storage tank by combining the dynamic change of the air cushion volume. S3. Establish a model relating liquid level and air cushion volume: Calculate the change in liquid level in the ground tank based on the main injection flow rate and vaporization flow rate, calculate the change in liquid level in the rocket tank based on the main injection flow rate, and obtain the real-time volume of the air cushions on both sides from the real-time liquid level. S4. Establish a flow calculation model for the delivery pipeline: Combine the pressure of the air pillow in the ground storage tank and the air pillow in the rocket storage tank, the static pressure of the liquid level and the position height to determine the available pressure difference of the pipeline, and calculate the main injection flow rate based on the pipeline resistance characteristics from the available pressure difference; S5. Dynamic Coupling Solution: The above models are coupled and associated to construct a dynamic equation system and perform numerical solution to obtain the dynamic parameters of pressure, liquid level and flow rate throughout the filling process.

[0007] Preferably, S1 specifically includes the following steps: S11. Establish the gas state equation for the ground storage tank's gas cushion and perform time differential to obtain the differential calculation formula for the gas cushion state quantity corresponding to the vaporization and pressurization process; The equation of state for the gas cushion of a surface storage tank is expressed as: The volume of the air cushion in the ground storage tank is... The pressure of the air cushion in the ground storage tank is The mass of gas inside the gas pillow of the ground storage tank is The compressibility coefficient of the gas in the ground storage tank is The gas constant is The gas temperature in the ground storage tank is The molar mass of the gas is ; The form after performing total time differentiation is: ; The state quantity of the air cushion of the ground storage tank is defined as follows: PV The final differential formula for the air cushion state quantity is: ; S12. The vaporization flow rate of liquid hydrogen entering the vaporizer is adjusted by regulating the opening of the vaporization branch regulating valve. The vaporization flow rate satisfies the following: ; in, For the flow characteristic function of the vaporization branch valve, These are valve characteristic parameters. The density of liquid hydrogen, For valve opening parameters, This refers to the vaporization flow rate; After complete vaporization, the liquid hydrogen flows back to the ground-based storage tank's gas pillow. The rate of change of gas mass within the gas pillow satisfies the following: ; S13. Substituting the gas mass change rate into the differential calculation formula for the gas pillow state quantity, we obtain the change rate of the gas pillow state quantity for the ground storage tank: ; After obtaining the state variables of the air cushion, the air cushion pressure of the ground storage tank is calculated by combining the real-time air cushion volume: .

[0008] Preferably, S2 specifically includes the following steps: S21. Establish the gas state equation of the air cushion in the rocket's storage tank and perform total time differential to obtain the differential calculation formula of the air cushion state quantity corresponding to the depressurization and exhaust process. The gas state equation for the rocket's propellant tank air cushion is expressed as: ;in, The pressure of the air cushion in the rocket's storage tank. The volume of the air cushion in the rocket's storage tank. The compressibility coefficient of the gas in the rocket's propellant tank. R The gas constant is The temperature of the gas in the rocket's storage tank. M For gas molar mass, The mass of gas inside the air cushion of the rocket's storage tank; The formal expression for the total differential in time is: ; The air cushion state quantity of the rocket's onboard storage tank is defined as follows: PV 3. The final differential formula for the air cushion state quantity is: ; S22. During liquid hydrogen refueling, gas in the gas cushion is discharged through the pressure relief channel of the rocket's storage tank. The gas discharge volume flow rate is calculated from the pressure relief channel parameters. Q 2. The rate of change of gas mass within the air cushion satisfies: ;in, This indicates the density of hydrogen gas inside the air cushion on the arrow; S23. Substituting the rate of change of gas mass into the differential calculation formula for the state quantity of the gas pillow, we obtain the rate of change of the state quantity of the gas pillow in the rocket's storage tank: ; After obtaining the air cushion state variables, the air cushion pressure in the rocket's storage tank is calculated based on the real-time air cushion volume. .

[0009] Preferably, step S3 specifically includes the following steps: S31. Constructing the liquid level change equation: During the liquid hydrogen refueling process, the liquid hydrogen in the ground storage tank is divided into two parts: one part is distributed according to the refueling flow rate. Q The other part is transported to the onboard storage tank, and the rest is transported at a vaporization flow rate. Q 1. Enters the vaporizer to participate in pressurization; the rate of decrease in the liquid level of the ground storage tank and the rate of increase in the liquid level of the onboard storage tank respectively satisfy: ; ; In the formula, h 1 represents the liquid level in the surface storage tank. Q Add more flow to the main source. Q 1 represents the vaporization flow rate. S 1 represents the current liquid surface area of ​​the ground storage tank; h 2 represents the liquid level in the rocket's onboard storage tank. S 2 represents the cross-sectional area of ​​the rocket's storage tank; S32. Calculate the liquid volume in both tanks based on the real-time liquid level, and subtract the liquid volume from the total volume of the corresponding tanks to obtain the real-time air cushion volume.

[0010] Preferably, in S32, the on-rocket storage tank is a cylindrical storage tank with a constant cross-sectional area, the cross-sectional area of ​​which satisfies: ;in, R 2 represents the radius of the rocket's onboard storage tank; The volume of the air cushion in the rocket's storage tank meets the following requirements: ;in, This refers to the total volume of the arrow's onboard storage tanks; h 2 represents the liquid level in the rocket's onboard storage tank; The above-ground storage tank is a horizontal cylindrical tank with a radius of [missing information]. R 1, length is H 1. The total volume of the storage tank meets the following requirements: ; The volume of liquid in a ground-level storage tank is the area of ​​the circular segment of the cylindrical cross-section corresponding to the liquid level. S ( h 1) Product with the length of the storage tank: ; The volume of the air cushion in the ground storage tank is: .

[0011] Preferably, in S4, the specific steps are as follows: S41. Calculate the inlet and outlet pressures of the delivery pipeline: ; ; in, P 2 represents the inlet pressure of the pipeline. ρ The density of liquid hydrogen, g It is the acceleration due to gravity. P 4 represents the pipeline outlet pressure. H 2 represents the height of the rocket's onboard storage tank above the ground; The pipeline can satisfy the following pressure differential: ;when At that time, the main injection flow rate is zero; S42, The cross-sectional area of ​​the conveying pipeline satisfies: ;in, d The diameter of the delivery pipeline; Based on the total pipeline resistance coefficient, the main injection flow rate satisfies: ;in, This is the friction coefficient. L This is the total length of the pipeline. This is the total local resistance coefficient of all regulating valves in the pipeline.

[0012] Preferably, in S42, the friction coefficient λ The flow rate is obtained by an iterative method: within each simulation time step, an initial value of the friction coefficient is given, the Reynolds number is calculated and the friction coefficient is updated accordingly, and then the flow rate is recalculated. The above steps are repeated until the relative deviation of the flow rate obtained from two adjacent calculations is less than a preset threshold. The Reynolds number is: ; The method for calculating the friction coefficient is as follows: ; in, μ Represents the dynamic viscosity of a fluid. v This indicates the average flow velocity inside the pipe. ε This refers to the roughness of the pipe.

[0013] Preferably, the total local drag coefficient The sum of the local resistance coefficients of each regulating valve, the first... i The local resistance coefficient of a control valve is determined by its opening degree. H i calculate: .

[0014] Preferably, in S5, the constructed system of dynamic differential equations is as follows: ; The equations are solved iteratively using the liquid level in the ground tank, the liquid level in the onboard tank, the state variables of the air cushion in the ground tank and the air cushion in the onboard tank as state variables, to obtain the dynamic parameters of the entire refueling process.

[0015] Therefore, this invention employs the aforementioned coupled modeling method for rocket liquid hydrogen refueling systems based on the gas equation of state. It establishes an overall coupled model between the ground storage tank, vaporization branch, delivery pipeline, and onboard tank. The state equation of the ground storage tank's gas pillow describes the influence of vaporizer return gas on the ground storage tank pressure, and the regulating valve of the vaporization branch describes the regulating effect of vaporization flow. Simultaneously, the state equation of the onboard tank's gas pillow and the pressure relief flow rate describe the pressure changes of the onboard gas pillow. Furthermore, the ground pressure, onboard pressure, liquid level, and pipeline resistance are used together to calculate the main refueling flow rate, thus forming a dynamic closed-loop model between pressure, liquid level, flow rate, and valves.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a diagram showing the liquid level changes in a ground storage tank according to an embodiment of the present invention; Figure 2 This is a diagram showing the liquid level change in the rocket's onboard storage tank according to an embodiment of the present invention; Figure 3 This is a diagram showing the volume change of the air cushion in the ground storage tank according to an embodiment of the present invention; Figure 4 This is a diagram showing the pressure variation of the air cushion in the ground storage tank according to an embodiment of the present invention; Figure 5 This is a diagram showing the volume change of the air cushion in the rocket's onboard storage tank according to an embodiment of the present invention; Figure 6 This is a diagram showing the pressure variation of the air cushion in the rocket's onboard storage tank according to an embodiment of the present invention; Figure 7 This is a graph showing the change in injection flow rate Q according to an embodiment of the present invention; Figure 8 This is a flowchart of the coupled modeling method for rocket liquid hydrogen refueling system based on the gas state equation of the present invention; Figure 9 This is a model diagram of the rocket liquid hydrogen refueling system of the present invention. Detailed Implementation

[0018] The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments. Unless otherwise defined, the technical or scientific terms used in this invention should be understood in their ordinary sense by those skilled in the art. The described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0019] Example 1 This embodiment provides a coupled modeling method for a rocket liquid hydrogen refueling system based on the gas equation of state. For example... Figure 8 The flowchart shown is a method of this embodiment. The method includes the following steps: establishing a ground storage tank air cushion pressurization model, establishing an on-rocket storage tank air cushion depressurization model, establishing a liquid level and air cushion volume correlation model, establishing a pipeline flow calculation model, and dynamic coupling solution. Figure 9 The diagram shown is a model of the rocket liquid hydrogen refueling system described in this embodiment, comprising four core units: a ground-based horizontal liquid hydrogen storage tank, a vaporization pressurization branch, a multi-regulating valve main delivery pipeline, and an onboard cylindrical liquid hydrogen storage tank; supporting branch systems include a vaporization return pipeline and an onboard hydrogen depressurization channel. The specific structural parameters of each unit are as follows: The surface storage tank is a horizontal cylindrical structure with a radius of... R 1 = 5m, tank length H 1 = 15m; The rocket's onboard storage tank is a vertical cylindrical structure with a uniform cross-section and a radius of... R 2 = 4m, effective total height 2m, rocket body height above ground H 2. Fixed; The vaporization branch is equipped with an independent regulating valve to control the flow rate of vaporized liquid hydrogen. Q 1; Three regulating valves are connected in series in the main filling pipeline, which together constitute the local resistance of the pipeline; The rocket's onboard storage tank is equipped with a pressure relief channel at the top, which allows hydrogen gas to be discharged and the pressure of the rocket's gas pillow to be controlled. P 3.

[0020] S1. Establish a pressurization model for the gas pillow in the ground storage tank: This step characterizes the state of the gas pillow in the ground storage tank based on the gas state equation, determines the mass change of the gas pillow based on the vaporization flow rate of the vaporization branch, and solves for the pressure of the gas pillow in the ground storage tank by combining the dynamic changes in the gas pillow volume. Specifically, it includes the following sub-steps: S11. Establish the gas state equation for the gas cushion of the ground storage tank and perform the total time differential: The volume of the air cushion in the ground storage tank is The pressure of the air cushion in the ground storage tank is The mass of gas inside the gas pillow of the ground storage tank is The compressibility coefficient of the gas in the ground storage tank is The gas constant is The gas temperature in the ground storage tank is The molar mass of the gas is The gas cushion of the ground storage tank satisfies the gas state equation: .

[0021] Taking the total differential of the above equation in time, we get: ; Gas volume change rate Caused by changes in the liquid hydrogen level, which are closely related to the injection flow rate and the vaporization process, the gas mass change rate in the gas pillow... The pressure and volume of the gas pillow in the ground storage tank can be dynamically calculated using the above model. This reflects the impact of the vaporizer completely vaporizing some of the liquid hydrogen on the pressurization process of the ground storage tank's gas pillow and provides a basis for simulation analysis and operation control of the filling process.

[0022] To facilitate numerical solutions, in this embodiment, the state variable of the ground storage tank air cushion is defined as follows: PV Therefore, the differential formula for calculating the state variables of the air cushion is: .

[0023] S12. Establish the relationship between vaporization flow rate and gas mass change rate: A vaporization branch regulating valve is installed between the ground storage tank and the vaporizer. This regulating valve determines the vaporization flow rate input to the vaporizer. Q 1. The vaporization flow rate meets the following requirements: ; in, For the flow characteristic function of the vaporization branch valve, These are valve characteristic parameters. The density of liquid hydrogen, This is the valve opening parameter, which can be determined based on valve design characteristics or test calibration results. When the valve opening decreases, the amount of liquid hydrogen entering the vaporizer decreases accordingly, thus affecting the hydrogen mass flow rate and pressurization capacity returning to the ground storage tank's gas pillow.

[0024] Assuming that the liquid hydrogen entering the vaporizer can be vaporized in a timely and complete manner and returned to the ground storage tank gas pillow, the rate of change of gas mass within the gas pillow satisfies: .

[0025] S13. Solve for the pressure of the air cushion in the ground storage tank: Substituting the rate of change of gas mass into the differential calculation formula for the gas pillow state quantity, we obtain the rate of change of the gas pillow state quantity for the ground storage tank: ; After obtaining the state variables of the air cushion, the air cushion pressure of the ground storage tank is calculated by combining the real-time air cushion volume: .

[0026] The above modeling method reflects the effect of the vaporizer vaporizing part of the liquid hydrogen on pressurizing the gas pillow of the ground storage tank.

[0027] S2. Establishing a depressurization model for the onboard gas cushion: This step characterizes the state of the onboard gas cushion based on the gas state equation, determines the gas mass change in the cushion based on the discharge flow rate of the depressurization channel, and solves for the onboard gas cushion pressure by combining the dynamic changes in the cushion volume. Specifically, it includes the following sub-steps: S21. Establish the gas state equation for the air cushion in the rocket's propellant tank and perform the total time differential: Assume the pressure of the air cushion in the rocket's storage tank is The volume of the air cushion in the rocket's storage tank is The compressibility coefficient of the gas in the rocket's propellant tank is [value missing]. The gas temperature of the air pillow in the rocket's storage tank is The mass of gas in the rocket's propellant tank is The gas state equation for the rocket's propellant tank air cushion is expressed as: ; Taking the total differential of the above equation in time, we get: ; The air cushion state quantity of the rocket's onboard storage tank is defined as follows: PV 3. The final differential formula for the air cushion state quantity is: .

[0028] S22. Establish the relationship between the pressure relief flow rate and the rate of change of gas mass: The rocket's onboard storage tank is equipped with a gas venting channel to discharge hydrogen from the gas pillow and suppress pressure rise in the gas pillow. Let the volumetric flow rate of hydrogen venting from the rocket's gas pillow be... Q 2. The density of hydrogen gas inside the air pillow is The rate of change of gas mass inside the air pillow is: .

[0029] S23. Solve for the pressure of the air cushion in the rocket's storage tank: Substituting the rate of change of gas mass into the differential calculation formula for the state quantity of the gas pillow, we obtain the rate of change of the state quantity of the gas pillow in the rocket's storage tank: ; After obtaining the air cushion state variables, the air cushion pressure in the rocket's storage tank is calculated based on the real-time air cushion volume. .

[0030] S3. Establish a correlation model between liquid level and air cushion volume: This step calculates the liquid level change in the ground storage tank based on the main injection flow rate and the vaporization flow rate, calculates the liquid level change in the on-rocket storage tank based on the main injection flow rate, and obtains the real-time volume of the air cushions on both sides from the real-time liquid level. Specifically, it includes the following sub-steps: S31. Constructing the liquid level change equation: During the liquid hydrogen refueling process, the liquid hydrogen in the ground storage tank is divided into two parts: one part is distributed according to the refueling flow rate. Q The other part is transported to the onboard storage tank, and the rest is transported at a vaporization flow rate. Q 1. The liquid enters the vaporizer to participate in pressurization; therefore, the liquid level in the ground tank continuously decreases, while the liquid level in the onboard tank continuously increases. The rates of decrease in the ground tank liquid level and the rates of increase in the onboard tank liquid level respectively satisfy: ; ; In the formula, h 1 represents the liquid level in the surface storage tank. Q Add more flow to the main source. Q 1 represents the vaporization flow rate.S 1 represents the current liquid surface area of ​​the ground storage tank; h 2 represents the liquid level in the rocket's onboard storage tank. S 2 represents the cross-sectional area of ​​the rocket's storage tank.

[0031] S32. Calculate the real-time air cushion volume: The volume of liquid in the two tanks is calculated based on the real-time liquid level. The volume of the air cushion is obtained by subtracting the liquid volume from the total volume of the corresponding tank.

[0032] During the liquid hydrogen refueling process, as the liquid level in the rocket's storage tanks rises... h 2. Increase the volume of the air cushion on the arrow. V 2. Gradually decreases. Assume the total volume of the onboard storage tanks is... The cross-sectional area of ​​the rocket's storage tank is S 2. The volume of the air cushion in the rocket's storage tank satisfies: ;in, ; R 2 represents the radius of the rocket's onboard storage tank.

[0033] The surface storage tank is a horizontal cylindrical tank with a liquid surface area of ​​[missing information]. With liquid level As it changes, let the radius of the ground storage tank be... , length is Based on the current liquid level Calculate the area of ​​the circular segment occupied by liquid hydrogen within the cross-section of the cylinder. S ( h 1) The volume of liquid in the ground storage tank is: ; The total volume of the surface storage tanks is: ; Therefore, the volume of the air cushion in the ground storage tank is: ; As the liquid level in the surface storage tank decreases, the volume of the air cushion in the surface storage tank gradually increases, and through... This further affects the change in air cushion pressure.

[0034] S4. Establish a flow calculation model for the delivery pipeline: This step determines the available pressure difference of the pipeline by combining the pressure of the air cushion in the ground storage tank and the air cushion in the rocket's storage tank, the static pressure of the liquid level, and the position and height. Based on the pipeline resistance characteristics, the main injection flow rate is calculated from the available pressure difference. Specifically, it includes the following sub-steps: S41. Calculate the available differential pressure in the pipeline: The ground storage tank, delivery pipeline, and onboard tank are considered as a liquid hydrogen interconnected system, with the ground storage tank's gas pillow pressure set at . The pressure of the air pillow in the rocket's storage tank is The density of liquid hydrogen is The acceleration due to gravity is The liquid level in the ground storage tank is The liquid level in the rocket's storage tank is The height of the rocket's storage tank above the ground is Then the inlet pressure and outlet pressure of the pipeline are respectively: ; ; This yields the available pressure differential in the delivery pipeline: ;when At that time, it was determined that liquid hydrogen could not continue to be delivered to the rocket's storage tank under the current operating conditions, and the main refueling flow rate was set to zero.

[0035] S42. Calculate the main injection flow rate: Let the diameter of the conveying pipeline be... d The cross-sectional area of ​​the filling pipe is: ; Let the friction coefficient be... The total length of the pipeline is L The total local resistance coefficient of multiple control valves is Then the main injection flow rate of the delivery pipeline meets the following requirements: .

[0036] Among them, friction coefficient λ The flow rate is obtained by an iterative method: within each simulation time step, an initial value of the friction coefficient is given, the Reynolds number is calculated and the friction coefficient is updated accordingly, and then the flow rate is recalculated. The above steps are repeated until the relative deviation of the flow rate obtained from two adjacent calculations is less than a preset threshold. The Reynolds number is: ; The method for calculating the friction coefficient is as follows: ; in, μ Represents the dynamic viscosity of a fluid. v This indicates the average flow velocity inside the pipe. ε This refers to the roughness of the pipe.

[0037] Multiple regulating valves are installed in the delivery pipeline. Let the first... i The opening degree of each regulating valve is H i The local resistance coefficient is then expressed using an empirical expression related to the valve opening degree as follows: .

[0038] The total local resistance coefficient of multiple control valves is the sum of the local resistance coefficients of each control valve: .

[0039] S5. Dynamic Coupling Solution: The above models are coupled and linked to construct a dynamic equation system and solve it numerically to obtain the dynamic parameters of pressure, liquid level, and flow rate throughout the entire refueling process. The specific dynamic coupling equation system for the liquid hydrogen refueling process is as follows: ; The four differential equations described above constitute the core dynamic model of the liquid hydrogen refueling process. The first equation describes the change in liquid level in the ground storage tank with the main refueling flow rate and the vaporization flow rate; the second equation describes the change in liquid level in the onboard tank with the main refueling flow rate; the third equation describes the pressure change of the ground storage tank's gas pillow under the action of vaporizer return gas; and the fourth equation describes the pressure change of the onboard tank's gas pillow under the action of pressure relief flow rate.

[0040] The equations are based on the liquid level in the ground storage tank. h 1. Liquid level in the rocket's storage tank h 2. Ground storage tank air cushion status quantity P 1 V 1. Air cushion status of the rocket's storage tank P 3 V 2 represents the state variable, which is solved iteratively using numerical integration to obtain the dynamic parameters of the entire injection process.

[0041] Ground storage tank air cushion pressure Air cushion pressure in the rocket's storage tank Surface storage tank liquid level Onboard tank liquid level and main betting flow A dynamic coupling relationship is formed between them. The pressure of the ground storage tank affects the refueling flow rate through the pipeline inlet pressure, and the pressure of the on-rocket storage tank affects the refueling flow rate in the opposite direction through the pipeline outlet pressure; the refueling flow rate further changes the liquid level at both ends and the volume of the gas pillow, thereby realizing the coupled modeling of the entire liquid hydrogen refueling process.

[0042] A dynamic simulation model of the liquid hydrogen refueling process was further established to verify the proposed coupled modeling method of ground storage tanks, vaporization branches, delivery pipelines and rocket tanks.

[0043] The simulation parameters are set as follows: the initial liquid level in the ground storage tank is 9m; the initial liquid level in the onboard tank is 0m, and the maximum filling rate is set to 90% to ensure that a certain amount of air cushion space is maintained in the onboard tank. The liquid hydrogen density is taken as 70kg / m³. 3 The acceleration due to gravity is taken as 9.8 m / s². 2 The initial air cushion pressure of the ground storage tank is set at 0.2 MPa, and the initial air cushion pressure of the onboard storage tank is set at atmospheric pressure. The diameter of the delivery pipeline is set at 0.1 m, the total length is set at 400 m, and the pipeline roughness is set at 1.5 × 10⁻⁶. -5 m, the dynamic viscosity of liquid hydrogen is taken as 1.3 × 10 m. -5Pa·s. Multiple regulating valves are installed in the pipeline. The opening degree of each valve is given a fixed value in the simulation, and the main injection flow rate is affected by the local resistance coefficient of the valve.

[0044] In the pressurization section of the ground storage tank, a vaporization branch regulating valve is installed, with the initial valve opening set to 100%, corresponding to a rated vaporized liquid hydrogen flow rate of [missing information]. m 3 / s. In the simulation, the flow rate of the vaporization branch changes with the valve opening, which is used to represent the flow rate of liquid hydrogen entering the vaporizer and vaporizing back to the ground storage tank gas pillow, thereby changing the state quantity and pressure of the ground storage tank gas pillow.

[0045] In the onboard propellant tank section, a state equation for the onboard gas pillow is established, and a pressure relief channel for the onboard propellant tank is set. In the simulation, the initial pressure of the onboard propellant tank gas pillow is taken as atmospheric pressure, the diameter of the pressure relief channel is set to 0.05m, and the flow coefficient is taken as 0.8. When the pressure of the onboard gas pillow is higher than the external atmospheric pressure, some hydrogen gas is discharged through the pressure relief channel.

[0046] During the simulation, the liquid levels in the ground tank, the liquid levels in the onboard tank, the state variables of the air cushion in the ground tank, and the state variables of the air cushion in the onboard tank are used as dynamic state variables. The refueling process is solved using a numerical integration method. At each moment, the inlet and outlet pressures of the pipeline are calculated based on the air cushion pressure in the ground tank, the ground liquid level, the air cushion pressure on the onboard tank, the liquid level on the onboard tank, and the difference in pipeline height. The available pressure difference in the pipeline is further calculated. When the available pressure difference is greater than zero, the main refueling flow rate is calculated based on the friction loss and local resistance. When the available pressure difference is less than or equal to zero, the main refueling flow rate is set to zero.

[0047] The total simulation duration was set to 1800s, and the output results included curves showing the changes over time for the ground tank level, the rocket tank level, the ground tank air cushion pressure, the rocket tank air cushion pressure, the ground tank air cushion volume, and the main injection flow rate.

[0048] Figure 1 For the liquid level of the ground storage tank h Figure 1 shows the change over time. The liquid level in the ground storage tank gradually decreases due to the outflow of main liquid hydrogen and vaporized liquid hydrogen.

[0049] Figure 2 For the liquid level in the rocket's storage tank h 2. The variation diagram shows that as the refueling time increases, the liquid level in the rocket's storage tank gradually rises due to the continuous inflow of liquid hydrogen.

[0050] Figure 3 The graph shows the volume change of the gas pillow in the ground storage tank. As the filling time changes, liquid hydrogen continuously flows out of the ground storage tank, so the volume of the gas pillow in the ground storage tank increases accordingly.

[0051] Figure 4 For the pressure of the ground storage tank PFigure 1 shows the change in pressure in the ground storage tank as the refueling time progresses, starting from the initial pressure and decreasing. Although the vaporized liquid hydrogen pressurizes the tank, the outflowing liquid hydrogen also increases the volume of the gas pillow. Under the parameters of this embodiment, the pressure reduction effect of the increased gas pillow volume is dominant, therefore the overall gas pillow pressure in the ground storage tank shows a downward trend.

[0052] Figure 5 The diagram shows the volume change of the onboard gas pillow. As the refueling time increases, liquid hydrogen continuously flows into the onboard tank, causing the liquid level in the onboard tank to rise, which in turn causes the volume of the onboard gas pillow to gradually decrease.

[0053] Figure 6 For the pressure of the rocket's onboard tank P 3. Change diagram: At the beginning of refueling, the volume of the gas pillow decreased due to the large amount of liquid hydrogen entering, and the gas inside the gas pillow had not been discharged in time. Therefore, there was a period of pressure rise in the early stage of refueling. However, as the gas in the gas pillow continued to flow out, the pressure of the gas pillow on the rocket gradually dropped and tended to stabilize.

[0054] Figure 7 Mainly add flow Q The change diagram shows that at the beginning of refueling, due to ground pressure... P 1 is much greater than the pressure on the arrow. P 3. Therefore, the injection flow rate is relatively large; however, with the increase in ground pressure... P The decrease in 1 leads to a decrease in pressure differential, and therefore the injection flow rate also gradually decreases.

[0055] Through the above simulation verification, the dynamic coupling relationship between ground tank pressure, on-rocket tank pressure, liquid level change and refueling flow rate can be observed, thereby verifying the ability of this method to describe the entire liquid hydrogen refueling process.

[0056] Therefore, this invention employs the aforementioned coupled modeling method for rocket liquid hydrogen refueling systems based on the gas state equation. By establishing the state equation of the gas in the ground storage tank's gas cushion and performing total differential over time, combined with the dynamic relationship between the gas cushion volume change rate and the gas mass change rate, coupled modeling of the gas cushion pressure and volume is performed. This enables continuous calculation of the change in gas cushion pressure in the ground storage tank during the refueling process, improving modeling accuracy from a physical perspective. The ground storage tank, refueling pipeline, and onboard storage tank are considered as a connected system. When calculating the refueling flow rate, the influence of the liquid column static pressure caused by changes in gas cushion pressure and liquid level height is considered simultaneously. Furthermore, the liquid level change is updated in conjunction with the mass conservation relationship, thereby achieving the linkage calculation of refueling flow rate and liquid level change, and fully realizing real-time monitoring of the liquid column and gas cushion pressure throughout the entire refueling process.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A coupled modeling method for a rocket liquid hydrogen refueling system based on the gas equation of state, characterized in that, Includes the following steps: S1. Establish a pressurization model for the gas pillow of the ground storage tank: characterize the state of the gas pillow of the ground storage tank based on the gas state equation, determine the gas mass change of the gas pillow according to the vaporization flow rate of the vaporization branch, and solve the gas pillow pressure of the ground storage tank by combining the dynamic change of the gas pillow volume. S2. Establish a pressure relief model for the air cushion of the rocket's propellant tank: characterize the state of the air cushion of the rocket's propellant tank based on the gas state equation, determine the mass change of the air cushion gas according to the discharge flow rate of the pressure relief channel, and solve the pressure of the air cushion of the rocket's propellant tank by combining the dynamic change of the air cushion volume. S3. Establish a model relating liquid level and air cushion volume: Calculate the change in liquid level in the ground tank based on the main injection flow rate and vaporization flow rate, calculate the change in liquid level in the rocket tank based on the main injection flow rate, and obtain the real-time volume of the air cushions on both sides from the real-time liquid level. S4. Establish a flow calculation model for the delivery pipeline: Combine the pressure of the air pillow in the ground storage tank and the air pillow in the rocket storage tank, the static pressure of the liquid level and the position height to determine the available pressure difference of the pipeline, and calculate the main injection flow rate based on the pipeline resistance characteristics from the available pressure difference; S5. Dynamic Coupling Solution: The above models are coupled and associated to construct a dynamic equation system and perform numerical solution to obtain the dynamic parameters of pressure, liquid level and flow rate throughout the filling process.

2. The coupled modeling method for rocket liquid hydrogen refueling system based on gas equation of state according to claim 1, characterized in that, S1 specifically includes the following steps: S11. Establish the gas state equation for the ground storage tank's gas cushion and perform time differential to obtain the differential calculation formula for the gas cushion state quantity corresponding to the vaporization and pressurization process; The equation of state for the gas cushion of a surface storage tank is as follows: The volume of the air cushion in the ground storage tank is... The pressure of the air cushion in the ground storage tank is The mass of gas inside the gas pillow of the ground storage tank is The compressibility coefficient of the gas in the ground storage tank is The gas constant is The gas temperature in the ground storage tank is The molar mass of the gas is ; The form after performing total time differentiation is: ; The state quantity of the air cushion of the ground storage tank is defined as follows: PV The final differential formula for the air cushion state quantity is: ; S12. The vaporization flow rate of liquid hydrogen entering the vaporizer is adjusted by regulating the opening of the vaporization branch regulating valve. The vaporization flow rate satisfies the following: ; in, For the flow characteristic function of the vaporization branch valve, These are valve characteristic parameters. The density of liquid hydrogen, For valve opening parameters, Vaporization flow rate; After complete vaporization, the liquid hydrogen flows back to the ground-based storage tank's gas pillow. The rate of change of gas mass within the gas pillow satisfies the following: ; S13. Substituting the gas mass change rate into the differential calculation formula for the gas pillow state quantity, we obtain the change rate of the gas pillow state quantity for the ground storage tank: ; After obtaining the state variables of the air cushion, the air cushion pressure of the ground storage tank is calculated by combining the real-time air cushion volume: .

3. The coupled modeling method for rocket liquid hydrogen refueling system based on gas equation of state according to claim 2, characterized in that, S2 specifically includes the following steps: S21. Establish the gas state equation of the air cushion in the rocket's storage tank and perform total time differential to obtain the differential calculation formula of the air cushion state quantity corresponding to the depressurization and exhaust process. The gas state equation for the rocket's propellant tank air cushion is expressed as: ;in, The pressure of the air cushion in the rocket's storage tank. The volume of the air cushion in the rocket's storage tank. The compressibility coefficient of the gas in the rocket's propellant tank. R The gas constant is... The temperature of the gas in the rocket's storage tank. M For gas molar mass, The mass of gas inside the air cushion of the rocket's storage tank; The formal expression for the total differential in time is: ; The air cushion state quantity of the rocket's onboard storage tank is defined as follows: PV 3. The final differential formula for the air cushion state quantity is: ; S22. During liquid hydrogen refueling, gas in the gas cushion is discharged through the pressure relief channel of the rocket's storage tank. The gas discharge volume flow rate is calculated from the pressure relief channel parameters. Q 2. The rate of change of gas mass within the air cushion satisfies: ;in, This indicates the density of hydrogen gas inside the air cushion on the arrow; S23. Substituting the rate of change of gas mass into the differential calculation formula for the state quantity of the gas pillow, we obtain the rate of change of the state quantity of the gas pillow in the rocket's storage tank: ; After obtaining the air cushion state variables, the air cushion pressure in the rocket's storage tank is calculated based on the real-time air cushion volume. .

4. The coupled modeling method for rocket liquid hydrogen refueling system based on gas equation of state according to claim 3, characterized in that, S3 specifically includes the following steps: S31. Constructing the liquid level change equation: During the liquid hydrogen refueling process, the liquid hydrogen in the ground storage tank is divided into two parts: one part is distributed according to the refueling flow rate. Q The other part is transported to the onboard storage tank, and the rest is transported at a vaporization flow rate. Q 1. Enters the vaporizer to participate in pressurization; the rate of decrease in the liquid level of the ground storage tank and the rate of increase in the liquid level of the onboard storage tank respectively satisfy: ； ； In the formula, h 1 represents the liquid level in the surface storage tank. Q Add more flow to the main source. Q 1 represents the vaporization flow rate. S 1 represents the current liquid surface area of ​​the ground storage tank; h 2 represents the liquid level in the rocket's onboard tank. S 2 represents the cross-sectional area of ​​the rocket's storage tank; S32. Calculate the liquid volume in both tanks based on the real-time liquid level, and subtract the liquid volume from the total volume of the corresponding tanks to obtain the real-time air cushion volume.

5. The coupled modeling method for rocket liquid hydrogen refueling system based on gas equation of state according to claim 4, characterized in that, In S32, the onboard storage tank is a cylindrical tank with a constant cross-sectional area, which satisfies the following: ;in, R 2 represents the radius of the rocket's onboard storage tank; The volume of the air cushion in the rocket's storage tank meets the following requirements: ;in, This refers to the total volume of the arrow's onboard storage tanks; h 2 represents the liquid level in the rocket's onboard storage tank; The above-ground storage tank is a horizontal cylindrical tank with a radius of [missing information]. R 1, length is H 1. The total volume of the storage tank meets the following requirements: ; The volume of liquid in a ground-level storage tank is the area of ​​the circular segment of the cylindrical cross-section corresponding to the liquid level. S ( h 1) Product with the length of the storage tank: ； The volume of the air cushion in the ground storage tank is: .

6. The coupled modeling method for rocket liquid hydrogen refueling system based on gas equation of state according to claim 5, characterized in that, In S4, the specific steps are as follows: S41. Calculate the inlet and outlet pressures of the delivery pipeline: ； ； in, P 2 represents the inlet pressure of the pipeline. ρ The density of liquid hydrogen, g It is the acceleration due to gravity. P 4 represents the pipeline outlet pressure. H 2 represents the height of the rocket's onboard storage tank above the ground; The pipeline can satisfy the following pressure differential: ;when At that time, the main injection flow rate is zero; S42, The cross-sectional area of ​​the conveying pipeline satisfies: ;in, d The diameter of the delivery pipeline; Based on the total pipeline resistance coefficient, the main injection flow rate satisfies: ;in, This is the friction coefficient. L This is the total length of the pipeline. This is the total local resistance coefficient of all regulating valves in the pipeline.

7. The coupled modeling method for rocket liquid hydrogen refueling system based on gas equation of state according to claim 6, characterized in that, In S42, the friction coefficient λ The flow rate is obtained by an iterative method: within each simulation time step, an initial value of the friction coefficient is given, the Reynolds number is calculated and the friction coefficient is updated accordingly, and then the flow rate is recalculated. The above steps are repeated until the relative deviation of the flow rate obtained by two adjacent calculations is less than a preset threshold. The Reynolds number is: ; The method for calculating the friction coefficient is as follows: ; in, μ Represents the dynamic viscosity of a fluid. v This indicates the average flow velocity inside the pipe. ε This refers to the roughness of the pipe.

8. The coupled modeling method for rocket liquid hydrogen refueling system based on gas equation of state according to claim 6, characterized in that, The total local resistance coefficient The sum of the local resistance coefficients of each regulating valve, the first... i The local resistance coefficient of a control valve is determined by its opening degree. H i calculate: 。 9. The coupled modeling method for rocket liquid hydrogen refueling system based on gas equation of state according to claim 6, characterized in that, In S5, the constructed system of dynamic differential equations is as follows: ； The equations are solved iteratively using the liquid level in the ground tank, the liquid level in the onboard tank, the state variables of the air cushion in the ground tank and the air cushion in the onboard tank as state variables, to obtain the dynamic parameters of the entire refueling process.

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